Download Retinal image quality in the rodent eye

Visual Neuroscience (1998), 15, 597–605. Printed in the USA.
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Retinal image quality in the rodent eye
PABLO ARTAL,1 PILAR HERREROS de TEJADA,2 CARMEN MUÑOZ TEDÓ,2
and DANIEL G. GREEN 3
1
Laboratorio de Optica, Departamento de Física, Universidad de Murcia, Murcia, Spain
Departamento de Psicobiologia, Universidad Complutense de Madrid, Madrid, Spain
3
Department of Ophthalmology, University of Michigan, Ann Arbor
2
(Received July 18, 1997; Accepted December 2, 1997)
Abstract
Many rodents do not see well. For a target to be resolved by a rat or a mouse, it must subtend a visual angle of a
degree or more. It is commonly assumed that this poor spatial resolving capacity is due to neural rather than optical
limitations, but the quality of the retinal image has not been well characterized in these animals. We have modified
a double-pass apparatus, initially designed for the human eye, so it could be used with rodents to measure the
modulation transfer function (MTF) of the eye’s optics. That is, the double-pass retinal image of a monochromatic
(l 5 632.8 nm) point source was digitized with a CCD camera. From these double-pass measurements, the
single-pass MTF was computed under a variety of conditions of focus and with different pupil sizes. Even with the
eye in best focus, the image quality in both rats and mice is exceedingly poor. With a 1-mm pupil, for example, the
MTF in the rat had an upper limit of about 2.5 cycles0deg, rather than the 28 cycles0deg one would obtain if the
eye were a diffraction-limited system. These images are about 10 times worse than the comparable retinal images in
the human eye. Using our measurements of the optics and the published behavioral and electrophysiological contrast
sensitivity functions (CSFs) of rats, we have calculated the CSF that the rat would have if it had perfect rather than
poor optics. We find, interestingly, that diffraction-limited optics would produce only slight improvement overall.
That is, in spite of retinal images which are of very low quality, the upper limit of visual resolution in rodents is
neurally determined. Rats and mice seem to have eyes in which the optics and retina0brain are well matched.
Keywords: Retinal image quality, Ocular modulation transfer function, Rodent eyes
acuity of 0.05 min 21 is so far from limits set by diffraction, even
with small pupils, that it is difficult to imagine that this acuity is
not simply a reflection of the coarse neural grain with which information is processed by the rat visual system. Consistent with
this, if one assumes that the rat retina is much like the human
peripheral retina and takes into account the differences in eye size,
the 8 cycle0deg resolution limit at 12 deg in the human peripheral
retina (Daitch & Green, 1969) corresponds to 1.3 cycles0deg in the
rat and 0.6 cycle0deg in the mouse, values which are very close to
the limits of what rats and mice can actually see (Birch & Jacobs,
1979; Sinex et al., 1979). Thus, one is inclined to think that the rat
and mouse retina is much like the human peripheral retina. It is
important to note in this regard that direct measurements in man
show that the low acuity in the near periphery is mainly due to the
neural processing and not to optical degradation of the peripheral
image (Green, 1970; Artal et al., 1995a; Williams et al., 1996).
Supportive evidence for optics being of relatively minor importance in limiting rat vision comes from Brown (1965) who reported that the size of the experimentally determined ganglion cell
receptive-field centers was comparable to the size of the anatomically determined dendritic tree of the ganglion cells. The receptivefield data was obtained using small spots of light which were
projected onto a screen in front of the animal (Brown & Rojas,
Introduction
It is well known that rodents have poor spatial vision (Lashley,
1938; Wiesenfeld & Branchek, 1976; Powers & Green, 1978; Birch
& Jacobs, 1979; Balkema & Pinto, 1982; Friedman & Green,
1982; Muñoz Tedó et al., 1992; Stone & Pinto, 1993). The evidence for this comes from both electrophysiological measurements
of the size of receptive fields and behavioral studies of visual
acuity. Recording from single optic tract units, for example, shows
that rat and mouse retinal ganglion cells have the classic centersurround receptive-field organization, but the fields are at least an
order of magnitude larger than those of the primate fovea (Brown,
1965; Green et al., 1977; Balkema & Pinto, 1982; Stone & Pinto,
1993). Rat behavioral acuity under optimum conditions is only
about 0.05 min 21 (Lashley, 1938; Wiesenfeld & Branchek, 1976;
Birch & Jacobs, 1979), more than 20 times worse than optimum
acuity in man. It is commonly assumed that the large size of the
receptive field and the poor acuity reflect neural processing and
not optical spread. Part of the reason for thinking this is that an
Correspondence and reprint requests to: Daniel G. Green, Neuroscience
Building, 1103 E. Huron Street, University of Michigan, Ann Arbor, MI
48104-1687, USA.
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1965). If optical spread were significantly enlarging the retinal
images of spots, then the measured receptive fields should have
been larger than the true physiological receptive fields.
However, the situation might not be quite so simple. When one
views the rat fundus with an ophthalmoscope, the images of the
retinal landmarks, such as fine blood vessels, do not appear to be
as sharp and clearly delineated as in man. Hughes and Wassle
(1979) have quantified these observations by using indirect ophthalmoscopy to view the retinal images of square-wave grating
targets. They reported that the double-pass retinal image was so
poor that at about 3 cycles0deg the contrast of the retinal image
dropped to zero. Given recent advances in the technology for
making objective measurements of retinal image quality using the
double-pass apparatus (Santamaría et al., 1987; Artal & Navarro,
1992; Artal et al., 1995b, Williams et al., 1996), we decided it was
appropriate to make detailed measurements of the double-pass line
spread in rats and mice. Such measurements had been made on the
cat eye (Bonds et al., 1972; Bonds, 1974), but not on rodent eyes.
One motivation for knowing what sets the limits to spatial resolution in rodent eyes is that small rodents have become increasingly more important as experimental animals as new developments
in genetics have created the potential for good rodent models of
hereditary human eye disease.
We report here that even with a 1-mm pupil, rat and mouse
retinal image quality is very poor relative to the limits imposed by
diffraction. With a 1-mm pupil, the image of a thin line spreads not
over several minutes of arc, as in man, but rather over as much as
several degrees of visual angle. It was surprising therefore to discover that in spite of the low quality of the image that is formed on
the retina, the optics of the eye does not set the limits for spatial
vision. In fact, the optics and the retinal properties seem to be
sufficiently well matched that better optics would lead to only very
slight improvements in the visual capacities of both rats and mice.
Thus, the situation is much like that in the fovea of man (Campbell
& Green, 1965), but on quite a different spatial scale.
Methods
Double-pass technique
An improved double-pass apparatus was developed to measure the
modulation transfer function in the human eye. The description of
this system along with the MTF results under different conditions
have been presented elsewhere (Santamaría et al., 1987; Artal &
Navarro, 1992, 1994; Navarro et al., 1993; Artal et al., 1995b,
Williams et al., 1996). The system we used in this work consists of
two stages: the recording of short-exposure coherent aerial images
of a point object after double pass through the eye; and digital
image processing, including averaging of aerial images, Fourier
transform, and computation of the square root to obtain the “single
pass” ocular MTF.
We have modified the double-pass apparatus for use in rodent’s
eyes. Fig. 1 shows a diagram of the experimental setup. The beam
coming from a red He–Ne laser (l 5 632.8 nm) of nominal power
(10 mW) first passes through an optional neutral density filter
(DF) used to attenuate and adjust the light intensity on the CCD
camera to the optimum range. The beam is spatially filtered by a
203 microscope objective (M). A 10-mm pinhole (P) acts as the
point object (O). The emerging beam is collimated by the lens LC
( f 9 5 200 mm); about 8% of the light is reflected towards the eye
by a pellicle beam splitter (BS). Before entering the eye, the beam
passes through a system consisting of two equal lenses L1–L2
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Fig. 1. Diagram of the experimental setup.
( f 9 5 120 mm). This allows use of an artificial pupil by imaging
the spot (AP2) on the animal’s pupil plane by the lenses L1–L2,
independent of their relative position. This provides a method to
modify the state of focus by moving backward and forward the
block (FB), to which the animal in the stereotaxic apparatus is
fixed. The animal’s eye is centered with respect to the measurement beam by using two translation stages (CB1, CB2) and the eye
is placed at one focal length distance from lenses L2 by using a
third translation stage (CB3). The animal’s eye forms the image of
the point O on the retina O9, and a small fraction of the light is
reflected back, passing again through the optical media of the eye
(second pass), lenses L1–L2, and the beam splitter (BS). Finally,
an objective lens (OB) ( f 9 5 28 mm) forms the aerial image O0 on
a CCD camera. The camera (Hitachi KP-140) along with the frame
grabber (Matrox MVP-AT) was previously calibrated. Each pixel
subtends 1.28 min of arc, with the whole 256 3 256 pixel images
covering nearly 5.5 deg of visual field. The double-pass retinal
image of the point test was monitored in real time (D2) allowing
us to control centering and other factors prior to digitizing and
storing the images using the frame grabber. The measurements
were obtained for different focus positions from 210 diopters to
15 diopters, adjusted by placing the block (FB) in different positions. The short-exposure aerial images were averaged to remove
speckle noise to simulate incoherent imaging conditions (Santamaría et al., 1987). In this particular study, we computed each MTF
from the average of 16 frames. The actual procedure is to take two
series of eight exposures each and compute the average afterwards.
Each snapshot is delivered by the experimenter when the desired
conditions are reached. The centering of the animal’s eye is checked
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before taking each image, and the resulting image is accepted only
when it is free of artifacts and the intensity is within a useful range.
A background image is obtained by placing a black diffuser in the
pupil plane instead of the eye and subtracted from the primary
image. After averaging the short-exposure retinal images, the remaining background is removed by subtracting the average intensity value computed in the four corners of the image. The Fourier
transform of the aerial image is computed, and the “single pass”
MTF is obtained as the square root of its modulus.
Animal manipulation
Six hooded Long Evans rats (four males and two females) 3 months
of age were used in these experiments and three male pigmented
(C57BL06J) mice of about the same age. The animals were anesthetized with i.p. injections of Equistesin (3 ml0gm). Supplementary doses were administered every 30 min. Body temperature was
maintained by placing the animal on a heating pad. All the measurements were from the animal’s right eye. The animal’s eyelids
were retracted with surgical silk thread. Animals were mounted on
a Kopf small-animal stereotaxic apparatus (model 900) that allowed for an unobstructed view of the right eye. A suture placed
through the conjunctiva allowed us to rotate the eyeball so as to
bring the axis of the eye into approximate alignment with the axis
of the measuring system. As Hughes (1977) had previously reported, we found that it was essential to keep the cornea moist.
Artificial tears were applied on a regular basis throughout the
experiments. Just before the collection of each set of data, a drop
was placed on the eye and the excess removed with a small piece
of absorbent tissue. An ancillary infrared viewing system allowed
us to monitor and measure the size of the animal’s pupils. After the
animal had been aligned, initial measurements could be made
through the natural pupil. In the anesthetized animal in a wellilluminated room, the pupil typically varied from about 1 to 2 mm
in diameter. Following these initial measurements the pupil was
dilated with atropine (1%). It took about 10 min for the pupil to
reach a fully dilated diameter of 3.5 and 4 mm. Additional measurements were then obtained through an artificial pupil projected
into the dilated natural pupil.
Results
Focus
In the first set of experiments, we attempted to determine the plane
of best focus in the rat’s eye. While the whole question of the
refractive state of the rat’s eye has been a matter of some controversy (see Hughes, 1977 for a review), our interest was simply in
determining what focus gave us the sharpest images. The approach
we took was to record double-pass images in each eye. Using the
double-pass line spread function, we determined how the width of
the double-pass image changed with varying focus. The vergence
of the incoming pencil of rays was varied by changing the position
of lens L2 and animal relative to lens L1 (Fig. 1). Sample doublepass aerial images from one animal are shown in Fig. 2. These
aerial images were formed on the CCD camera with pupil diameters of 1 and 2 mm and 612 diopter extremes in the vergence of
the incoming bundle. The images on the left, labelled hyperopic,
are for a converging incoming bundle of rays (18.4 diopters) and
those on the right are for a diverging bundle (28.4 diopters). These
images are more or less radially symmetrical, as were all the
double-pass images we obtained. For both pupil sizes illustrated,
Fig. 2. Two-dimensional double-pass images of a rat’s eye for two pupil
diameters and two refractions (8.4 diopters on the left and 28.4 diopters on
the right). The upper images are for a 1-mm pupil and the lower images for
a 2-mm pupil.
the double-pass images were narrowest when the eye was hyperopic. Fig. 3 shows one-dimensional double-pass line functions for
the aerial images shown in Fig. 2. They were obtained from the
two-dimensional point spread function by integrating the measurements vertically. As Figs. 2 and 3 demonstrate, the images were
sharper when the eye was hyperopic. The question which remains
unanswered is where exactly was the eye focused? To establish
this, measurements of the retinal image were made in which focus
was systematically varied over a range of 28.4 to 12.6 diopters.
From each of the double aerial point spread functions, a horizontal
double-pass line spread function was computed. Using these line
spread functions, we determined the width of the double-pass image at half-height. The results of such measurements with two
pupil sizes in three pigmented rats are shown in Fig. 4. Panel A,
on the left, is for a 1-mm pupil, and panel B, on the right, is for a
2-mm pupil. With a 1-mm pupil, the width of the double-pass
functions are quite flat, particularly on the positive (hyperopic)
side of emmetropia. For the vergence of the incoming rays varying
between 0 and 18.4 diopters, the width of the double-pass spread
function did not vary by more than 10%. In other words, over this
whole range the changes are so small that the image is really in
equivalent focus. In this regard, it is important to note that we have
plotted the width of the double-pass point spread function. The
actual changes in the quality of the image on the retina, the singlepass spread function, would be expected to be still smaller (see
Fig. 8 for a comparison of single- and double-pass point spread
functions). This great depth of focus is consistent with 610 diopters predicted by Green et al. (1980). Nonetheless, there was a
clear tendency for the image to be sharper at 8.4 than at 0 diopters.
With 2-mm-diameter pupils, the image quality was considerably worse. The double-pass spread functions were about a factor of
two broader than with the 1-mm pupil. In addition, the tendency for
the images to be sharper when the bundle of incoming rays was hyperopic was much clearer. There were also larger differences between animals with the 2-mm pupils than with the 1-mm pupils.
These differences could be due to differences in the refractive state
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Fig. 3. One-dimensional double-pass line spread functions. (a) 1-mm pupil diameter (28.4 diopters—solid line and 8.4 diopters—
dashes), and (b) 2-mm pupil diameter (from double-pass images illustrated in Fig. 2).
with the larger pupils. The animal shown with squares was 5 diopters more hyperoptic (and the animal shown with circles was 10
diopters more hyperopic) than the animal shown with the triangles.
Fig. 5 shows some results for a mouse. A typical double-pass
line spread function is plotted in Fig. 5a. If one compares this with
the line spread functions of Fig. 3, it is clear that the width of the
double-pass spread function in the mouse is nearly three times as
broad as that in the rat. Fig. 5b shows that, in addition to the overall
image quality being worse in the mouse, there seems to be less of
a tendency for the width of the spread function to change with
refraction, as would be expected for a smaller eye (Green et al,
1980).
Accommodation
It is generally believed that the rat cannot accommodate. Rats are
reported to lack the ciliate muscles required to change the curvature of the ocular lens. Also one might argue that since the rat eye
is already so hyperemic, any change in refractive power would do
little to bring near targets into better focus. Nonetheless, we decided to take advantage of the opportunity we had of testing for
accommodative ability by comparing the changes in the doublepass image size with focus with “unparalyzed” accommodation
and with accommodation “paralyzed” with atropine. Fig. 6 shows
a comparison of the width of the recorded double-pass images as
Fig. 4. Width at half-height in the double-pass images for three animals for two pupil diameters (1-mm pupil in left panel and 2-mm
pupil in right panel).
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Fig. 6. Width at half-height of the double-pass line spread functions as a
function of focus for one rat with atropine (solid line) and without atropine
(dashed line), for two pupil diameters (1 and 2 mm).
Fig. 5. (a) One-dimensional double-pass line spread functions for 1-mm
pupil diameter and best focus in a mouse. (b) Width at half-height in the
double-pass retinal images of a mouse for two pupil diameters, with artificial pupils, and atropine.
a function of focus in the same animal with and without atropine,
for 1- and 2-mm pupil diameters. We found no significant changes
with atropine. The width of the double-pass line spread function
consistently was slightly smaller with the natural pupil. This could
be due to the natural pupil actually being a little smaller than the
artificial pupil or to the natural pupil being better centered than the
artificial pupil. The absence of any indication of a change in refractive power with atropine is consistent with the rat lacking the
ability to accommodate. These experiments, of course, showing
that atropine produces no additional change in refractive power, do
not prove that the rat does not have the ability to accommodate,
since under these conditions of anesthesia accommodation could
already be fully relaxed.
Single-pass optical quality
What is the quality of the retinal image in the rat (and mouse)? To
do this, we have taken the double-pass aerial images and used them
to calculate modulation transfer functions. Fig. 7 shows the aver-
age modulation transfer functions with 1- and 2-mm pupils, on
linear scales (a) and on a logarithmic modulation scale (b). From
these MTFs, it is relatively straightforward to calculate the (singlepass) point spread of the eye. Fig. 8 shows the average point spread
function obtained in four rats for the conditions of best focus (8.4
diopters hyperopic) with a pupil size of 1 mm. The single-pass
point spread function has two components, a relatively narrow
peak (about 3 minutes of arc half-width) and a broad pedestal.
Fig. 9 shows the MTFs for one rat at the extremes of hyperopic and
myopic. The optical quality in the rodents’ eyes in comparison
with those in the human eye is exceedingly poor.
The MTF with the 1-mm pupil fell to less than 0.1 at about 2.0
cycles0deg. Fig. 10 further illustrates the differences between rodents and man by comparing human and rat and mouse MTFs. The
MTF of the mouse has a high frequency cutoff of only 1.0 cycle0
deg. Since the rat’s eye is about one fifth the size of the human eye,
we have compared the MTFs measured with the 4-mm pupil with
the measurements at 1 mm, so that the numerical apertures are
approximately equivalent. Fig. 10 also shows measurements that
were obtained in the mouse eye with a 1-mm pupil.
MTF calculations from a rat’s model eye: Comparison
with the measured MTFs
It is of interest to know how our measurements compare with what
might be expected. To address this, we have used a simple model
of the rat’s eye to calculate the retinal MTF. We performed the
calculations by using the ZEMAX XE optical design software
(Focus Software, Tucson, AZ). The rat’s eye was modeled by a
series of spherical refracting surfaces. The curvatures and positions
of the refracting surfaces of the rat’s eye were taken from Block
(1969). Figs. 11a and 11b show a comparison of calculated and
measured MTFs for 1- and 2-mm pupils. The model correctly
predicts that image quality is much worse than the diffraction limit,
with a 2-mm pupil. The calculated and measured MTFs agree
reasonably well below 1 cycles0deg, but the measurements systematically fall below the calculations at higher spatial frequencies. This may be due to the point spread function being a sum of
a narrow function, which is accounted for by the model, and a
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Fig. 8. Average double- (solid line) and single-pass (dashed line) point
spread functions for rats.
vergence of the source over a range of 21 diopters (28.4 to 12.6
diopters). This corresponds to object distances from 12 cm in front
of the eye to way beyond optical infinity. We found only a very
weak dependence of image quality on focus, with a tendency for
the spread function to get slightly narrower when the eye was
extremely hyperopic. Thus rodent eyes have great depth of focus.
We did not make measurements under still more hyperopic conditions. While it seems possible that the image might be a little bit
sharper with greater hyperopia, any such improvement in image
quality would have to be very small. Such improvement, if it
occurred, would be of no physiological relevance to an animal that
must view things in the space between its eyes and optical infinity.
Fig. 7. Average modulation transfer functions with 1-mm (solid line) and
2-mm pupils (dashed line) in best focus (8.4 diopters hyperopic). (a) On a
linear modulation scale. (b) Same data over an expanded spatial-frequency
range on a logarithmic modulation scale. The curves are the averages from
four rats.
broad function which adds a wide pedestal (see Fig. 8), which is
not accounted for by the model. Thus, the loss in image quality is
not completely explained by simple spherical aberration. In the
small eye of the rat, 2 mm corresponds to 6 mm in man. In the
human eye with a 6-mm pupil, higher order aberrations cause
significant deviations from the diffraction limit (Campbell & Green,
1965). Fig. 11c shows that the model eye exhibits great depth of
focus. The calculated image modulation at 2 cycles0deg changes
very little when focus varies from 28 to 16 diopters.
Discussion
We began by determining the refractive state of the rat. To find the
refraction that produced the sharpest retinal images, we varied the
Fig. 9. MTFs for a single animal with extremes of hyperopia and myopia
(28.4 diopters—dashed line and 8.4 diopters—solid line, respectively).
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Fig. 10. MTFs on logarithmic scales of a rat (solid line), a mouse (dotdashed line), and a typical human observer (dashed line).
Hyperopia has been found previously by those using other retinoscopic techniques. It has been suggested that the hyperopia seen
in small eyes arises because the light that returns comes from the
vitreal-retinal surface which is 100–150 mm in front the photoreceptors (Glickstein & Millodot, 1970). There is nothing in this
study for or against this idea. We accept that this, in addition to the
fact the measuring light is a 632.7-nm laser, may explain the 10–15
diopters of hyperopia. It is said that rats and mice lack the ability
to accommodate. When we examined the effect that atropine had
on the state of focus, we saw no changes. This is consistent with,
but does not prove, inability to accommodate.
The detailed measurements of the optical quality of the retinal
images in the rat and the mouse are new and potentially interesting
findings. Moreover, it was surprising to discover that in comparison to images in other animals the quality of the retinal image in
rodents was very poor. In man with a 1-mm pupil, the retinal image
is essentially diffraction limited, i.e. the cutoff frequency is 30
cycles0deg. In rat, the cutoff is closer to 1.5 or 2.0 cycles0deg. In
mice, the quality was still worse with the optical limit being close
to 1.0 cycle0deg. One of the limitations of the double-pass technique is that it does not measure the broad veiling pedestal of light
that the direct measurements of Robson and Enroth-Cugell (1978)
showed to exist in the cat’s eye. This is particularly true in these
experiments where a background image, obtained by placing a
black diffuser in the pupil plane instead of the eye, was subtracted
from the primary image and the remaining background was removed by subtracting the average intensity value computed in the
four corners of the image. Thus, the broad veiling pedestal that
must surely exist in the rodent’s eye has not been measured. Thus,
the MTFs we present here almost certainly overestimate the true
contrast at each spatial frequency by some small but unknown
factor.
Are these poor images the cause of the poor spatial resolving
abilities of mice and rats? The fall in optical performance with
increasing spatial frequency is always due to a combination of
optical and neural factors. The question is, in the rat, how much of
this fall is contributed by optics as opposed to neural processing?
To address this issue one needs to compare the optics with the
Fig. 11. Calculated (solid line) and measured MTFs (dashed line). (a) For
a rat in best focus with 1-mm pupil. (b) For a rat in best focus with 2-mm
pupils. (c) The calculated change in modulation at 2 cycles0deg produced
by various amounts of defocus. The calculations are for the rat’s eye with
a 1-mm pupil.
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overall contrast sensitivity function. Birch and Jacobs have measured the contrast sensitivity function (CSF) of rats using behavioral methods and their measurements are well fitted by the function
CSF 5 k1 exp~2k2 f !,
(1)
where k1 is a constant that depends on the average intensity, k2 5
2.88 deg0cycle, and f is spatial frequency in cycles0deg. Fig. 12a
compares our measured MTF with their CSF. Both are drawn on a
linear spatial-frequency axis. The modulation of the optical image
is plotted on the left vertical axis and contrast sensitivity is plotted
on the right axis. Surprisingly, even though the retinal image is of
poor quality, the optical MTF falls more slowly with increasing
spatial frequency than the CSF. These measurements suggest that
optics is not the major factor limiting visual resolution. At 1 cycle0
deg, close to the limit of resolution, the behavioral contrast sensitivity function of Birch and Jacobs has fallen by a factor 20. Our
measurements of the optical MTF(circles in Fig. 12a) show that at
1 cycle0deg the optics causes about a factor of 2 reduction in
contrast on the retina. Thus, the majority of the reduction, the
remaining factor of 10, must be due to the neural processing.
Another way of looking at the effect of the optics is to use the
measured optical MTF to calculate what the CSF would be if the
optics were perfect. This result is also shown in Fig. 12 (the triangles). When one compares the CTF the eye could achieve with perfect optics (triangles), against the actual CTF (squares), it is apparent
that better optics would lead to only small improvements in acuity.
Perfect optics would increase resolution by only one Snellian line.
Thus, the optics and visual capacities are matched in the sense that
the optics are not much better than they need be to cause vision to
be primarily limited by neural factors.
The situation is reminiscent of the human fovea where Campbell and Green (1965) found that at higher spatial frequencies the
attenuation due to the nervous system was twice as great as that
due to the optics. This kind of arrangement makes good sense from
an evolutionary perspective. If the reverse were true, that is if
better optics would lead to better vision, then evolutionary pressure
would be expected to select those animals with better optics. On
the other hand, there is nothing to be gained by having fine spatial
detail present in the retinal image if the neural apparatus cannot
process this information. In this context, the poorer optical quality
in the mouse is consistent with its lower spatial resolving capacities. This matching of the optical quality to the spatial abilities of
retina–brain seems to be a general finding. In cat, frog, rat, and
mouse (Wassle, 1971; Bonds, 1974; Robson & Enroth-Cugell,
1978; Krueger & Moser, 1971; and present study), where the visual capabilities are less than those of man, the optical quality of
the retinal image is progressively worse. On the other hand, in the
eagle, which has foveal resolving capacities greater than in the
human fovea, the optical quality is higher than in the human fovea
(Shlaer, 1972). In this context, we may tend to take for granted the
ability of living creatures to specialize and refine cellular structures so that they are sufficiently clear, smooth, and regular to form
good optical images on their retinas. It would seem that there is a
cost associated with doing this and the cost is sufficiently great that
each organism does no better in refining the optical quality of its
dioptric apparatus than necessary.
One aspect of this work puzzled us. What is causing the images
in the rat to be so poor? Could it simply be the small eye itself? To
address this issue, we traced rays through an optical model of the
rat’s eye consisting of a series of smooth spherical surfaces with
curvatures and indices that come from the rat schematic eye of
Block (1969), Campbell and Hughes (1981), and Hughes (1979).
For a 1-mm pupil, these calculations give the MTFs plotted in
Fig. 11. While the agreement is not perfect, it is better than we
expected, particularly since no aberrations other than simple spherical aberration have been included in the model. Thus, it seems that
in a small eye simply having strongly curved spherical refracting
surfaces can be sufficient to cause poor retinal images, and thus
one might not expect small eyes to have high acuity. This is not the
complete story of why rodent optical images are poor. In addition
to having highly curved spherical refracting surfaces, rat and mouse
eyes must have higher order aberrations that cause image quality to
be worse than what we calculate from our model eye.
Fig. 12. Effect of optics on rat contrast sensitivity. (a) The average modulation transfer function of the rat (from Fig. 8) is plotted with
circles. The normalized behavioral contrast sensitivity of the pigmented rat (after Birch & Jacob, 1979) is plotted with squares. The
computed retinal contrast is plotted with triangles. (b) A comparison of the actual contrast sensitivity of the hooded rat (squares) with
what would be expected if the optics were perfect (triangles).
Retinal image quality in the rodent eye
Acknowledgments
This research was supported by a NATO collaborative research grant to P.
Artal and D.G. Green (CRG 940081); a grant from DGICYT, Spain, to P.
Artal (PB94-M38-CO2-01); and a grant from the National Institutes of
Health, US Public Health Service to D.G. Green (EY 00379).
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